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David C,

I downloaded the source code of skyalmanac (this is what thenauticalalmanac.com uses):

https://github.com/aendie/SkyAlmanac-Py3
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"Skyalmanac-Py3 is a Python 3 script that creates the daily pages of the Nautical Almanac as well as Lunar Distance tables and charts.
...
it is based entirely on the newer Skyfield astronomical library: https://rhodesmill.org/skyfield/. Skyalmanac uses the star database in Skyfield, which is based on data from the Hipparcos Catalogue.
...
The results have been crosschecked with USNO data to some extent."
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From https://rhodesmill.org/skyfield/
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"Skyfield computes positions for the stars, planets, and satellites in orbit around the Earth. Its results should agree with the positions generated by the United States Naval Observatory and their Astronomical Almanac to within 0.0005 arcseconds (half a “mas” or milliarcsecond)."
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If I understand correctly the Astronomical Almanac (planetary/lunar data) is derived from JPL ephemeris DE430.
This code uses DE421 by default, but can be changed:

From config.py:
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# choose an ephemeris (ephndx = 0, 1, 2, 3 or 4):
#   0   de421.bsp   1900 to 2050
#   1   de405.bsp   1600 to 2200
#   2   de406.bsp   1000 to 2750 (Equation of Time may show ??:?? after 2750)
#   3   de430t.bsp  1550 to 2650
#   4   de440.bsp   1550 to 2650
ephndx = 0
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Based on these, it seems to me that it contains accurate data. Of course, a regular crosscheck with USNO data would be better.
Bela